A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

I'm glad you put this question up because I'm really not very good at rate/time/distance questions especially when they involve different variables, times, etc.

My guess is that the answer is A, 12 m/s.

At first I was trying to figure out what runner A's time (T) was but I couldn't get it to work. But since I knew that runner B's time was T-2 for 336 meters and T+6 for 432 meters, I thought that the difference between the heats for runner B would be 8 seconds. I know this a long way of doing this but I checked the answers to find out which rate would result in a difference of 8 seconds for the two different times. That's how I got A. The 336m run would take B 28 seconds and the 432m run would take B 36 seconds for a difference of 8 seconds.

Is that correct? If not, please let me know. If it is correct, then is there a faster way to get the answer? Thanks for posting these questions.

A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

Here's my solving method. Pay attention to units -- I suggest not to solve the 48-which is 10% of 480 and 144 (30%) until the very end.

By the formula D= S * T
we get two equations
480/Sa = 432/Sb -6 ------------1)
480/Sa = 336/Sb +2------------2)
Equating these two equations we get Sb = 12
ta,Sa stand for time taken by A and speed of A resp.

A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is B's speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

distance = 480m = d
B is given head start of 48 meters (which is 10% of 480) or we can say that B travels .9d
time taken by A = t sec and thus time taken by B = t+6 (=1/10 of a minute = 6 seconds)
B is given head start of 144 meters (30% of 480) or B travels .7d
time taken by A = t sec and time taken by B = t-2 (B beats A by 1/30 of a minute which is 2 seconds)
speed of B = distance/time = (.9d)/(t+6) = (.7d)/(t-2)
9t-18 = 7t + 42
=> t=30
Thus speed of B = .9d/(t+6) = .9*480/36 = 12 m/sec

A and B ran a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. What is Bï¿½s speed in m/s?
(A) 12
(B) 14
(C) 16
(D) 18
(E) 20

We can plug in the answers, which represent B's rate.
The correct answer must be a factor of 480.
Eliminate B and D.

In the first heat, A beats B by (1/10)*60 = 6 seconds.
In the second heat, B beats A by (1/30)*60 = 2 seconds.

Answer choice C: B = 16 meters per second.
First heat:
Time for B = d/r = 480/16 = 30 seconds.
Headstart given to A = 48/16 = 3 seconds.
Since A beats B by 6 seconds, total time for A = 30-(3+6) = 21 seconds.
21 is not a factor of 480.
Eliminate C.

Second heat:
Headstart given to B = 144/12 = 12 seconds.
From the first heat: Time for B - Time for A = 40-30 = 10 seconds.
Since B is given a 12-second headstart, and the time for A is only 10 seconds less than the time for B, B beats A by 12-10 = 2 seconds.
Success!

The correct answer is A.

_________________Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
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Can you please elaborate on how you arrived at the premise that speeds of both A and B should to be factors of 480.

Thanks

When the given times are converted into seconds, the results are integers:
1/10 of a minute = 6 seconds.
1/30 of a minute = 2 seconds.

Thus, the correct rate for B almost certainly will be a factor of the distance; otherwise, the resulting times will not be integer values.
Since the distance is 480, the correct answer should be a factor of 480.

_________________Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Contact me about long distance tutoring!